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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Growth of solutions of second order linear differential equations


Authors: Ilpo Laine and Pengcheng Wu
Journal: Proc. Amer. Math. Soc. 128 (2000), 2693-2703
MSC (1991): Primary 34A20; Secondary 30D05, 30D20, 30D35
Published electronically: March 1, 2000
MathSciNet review: 1664418
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the differential equation $f''+A(z)f'+ B(z)f=0$, where $A(z)$ and $B(z)$ are entire functions. Provided $\rho (B)<\rho (A)$ and $T(r,A)\sim \log M(r,A) $ as $r\to \infty $outside a set of finite logarithmic measure, we prove that all nonconstant solutions $f$ of this equation are of infinite order.


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Additional Information

Ilpo Laine
Affiliation: Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland
Email: Ilpo.Laine@joensuu.fi

Pengcheng Wu
Affiliation: Department of Mathematics, Nationality Institute of Guizhou, Guiyang, 550025, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05350-8
PII: S 0002-9939(00)05350-8
Keywords: Differential equation, entire function, finite order, Nevanlinna characteristic
Received by editor(s): August 18, 1998
Received by editor(s) in revised form: October 27, 1998
Published electronically: March 1, 2000
Additional Notes: This work was supported in part by the Finnish Academy research grant 37701.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society